Correct Answer - Option 1 : (at², 2at)
Calculation:
Parabola |
Parametric
equation
|
y2 = 4ax |
(at2, 2at)
|
y2 = -4ax
|
(-at2, 2at)
|
x2 = +4ay
|
(2at, at2)
|
x2 = -4ay
|
(2at, -at2)
|
(y - k2) = 4a(x - h)
|
(h + at2, k + 2at) |
(y - p2) = 4b(y - q)
|
(p + 2at, q + at2)
|
Here, the given parabola is y
2 = 4ax
So, its parametric coordinate is (at², 2at)
We can check it by putting the above point in the equation of parabole
L.H.S = y2
⇒ (2at)2
⇒ 4a2t2 -----(i)
R.H.S = 4ax
⇒ 4 × a × at2
⇒ 4a2t2 -----(ii)
From (i) and (ii), we get
∴ (at², 2at) is the parametric coordinates of the parabola y2 = 4ax.